Question

7.
The H.C.F of (24, 36) is 'd'. Such that d = 24a + 36b, then (a, b) =
A) (2,5)
B) (5,2)
C) (3,5)
D) (5, - 3)​

Answer 1

Answer:

Option (D)

Step-by-step explanation:

For this let us find HCF is 24,36

24 = 2*2*2*3

36 = 2*2*3*3

So here common factors are 2, 2, and 3

So HCF of 24 and 36 = 2*2*3 = 12

This means d=12

According to question,

d = 24a+36b

12 = 24a+36b

1 = 2a+3b

Now let us substitute the values in the options and see

If a=2 and b=5, then

1= 2*2+3*5 ...... it is not possible.. So option (A) is wrong

If a=5 and b=2, then

1=2*5+3*2...... it is not possible.. So option (B) is wrong

If a=3 and b=5, then

1=2*3+3*5..... it is not possible.. So option (C) is wrong

If a=5 and b=-3, then

1=2*5+3*-3 = 10-9 = 1 .... it is possible

So correct option is (D)

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